Method and an apparatus for a transmission scheme

ABSTRACT

According to an aspect, there is provided an apparatus for performing beamforming optimization for a MIMO architecture. The apparatus maintains, in a database, channel state information of a plurality of radio channels comprising first and second order statistics. The apparatus calculates, separately for each of two or more remote radio units using an eigenbeamforming scheme, first sets of beamforming weights based on the second order statistics. Then, the apparatus performs, for each terminal device, single-user MIMO optimization between the two or more remote radio units to maximize a pre-defined metric, being a mutual information metric or signal-to-interference-plus-noise, based on first sets of beamforming weights and the first order statistics. The result, for each terminal device, is a second set of beamforming weights. The apparatus causes transmitting data using beams formed by applying both first and second sets of optimized beamforming weights at the two or more remote radio units.

TECHNICAL FIELD

Various example embodiments relate to wireless communications.

BACKGROUND

The 5G massive MIMO uses beamforming in order to maximize antenna gainfor users. These schemes are essential for obtaining high gain withmassive MIMO systems. Distributed MIMO has been suggested for furtherimproving the performance. In distributed MIMO, multiple radio units (orequally remote radio units) are arranged in different locations within acell. In other words, instead of all the antennas associated with thecell being co-located, they are distributed. Consequently, indistributed MIMO, the beamforming scheme needs to be applied to severalMIMO antenna arrays (i.e., antenna panels) which are not calibrated witheach other and relative responses of which cannot be assumed to bestatic over longer periods. This places additionally challenges to theapplication of the beamforming schemes.

Thus, there is a need for a beamforming solution which would providehigh performance without excessive computational complexity usingdistributed MIMO.

BRIEF DESCRIPTION

According to an aspect, there is provided the subject matter of theindependent claims. Embodiments are defined in the dependent claims. Thescope of protection sought for various embodiments of the invention isset out by the independent claims.

The embodiments and features, if any, described in this specificationthat do not fall under the scope of the independent claims are to beinterpreted as examples useful for understanding various embodiments ofthe invention.

BRIEF DESCRIPTION OF DRAWINGS

In the following, example embodiments will be described in greaterdetail with reference to the attached drawings, in which

FIGS. 1 and 2 illustrate exemplary wireless communication systemsaccording to embodiments;

FIGS. 3, 4A, 4B and 5 illustrate exemplary processes according toembodiments; and

FIG. 6 illustrates an apparatus according to embodiments.

DETAILED DESCRIPTION OF SOME EMBODIMENTS

The following embodiments are only presented as examples. Although thespecification may refer to “an”, “one”, or “some” embodiment(s) and/orexample(s) in several locations of the text, this does not necessarilymean that each reference is made to the same embodiment(s) orexample(s), or that a particular feature only applies to a singleembodiment and/or example. Single features of different embodimentsand/or examples may also be combined to provide other embodiments and/orexamples.

In the following, different exemplifying embodiments will be describedusing, as an example of an access architecture to which the embodimentsmay be applied, a radio access architecture based on long term evolutionadvanced (LTE Advanced, LTE-A) or new radio (NR, 5G), withoutrestricting the embodiments to such an architecture, however. It isobvious for a person skilled in the art that the embodiments may also beapplied to other kinds of communications networks having suitable meansby adjusting parameters and procedures appropriately. Some examples ofother options for suitable systems are the universal mobiletelecommunications system (UMTS) radio access network (UTRAN orE-UTRAN), long term evolution (LTE, the same as E-UTRA), wireless localarea network (WLAN or WiFi), worldwide interoperability for microwaveaccess (WiMAX), Bluetooth®, personal communications services (PCS),ZigBee®, wideband code division multiple access (WCDMA), systems usingultra-wideband (UWB) technology, sensor networks, mobile ad-hoc networks(MANETs) and Internet Protocol multimedia subsystems (IMS) or anycombination thereof.

FIG. 1 depicts examples of simplified system architectures only showingsome elements and functional entities, all being logical units, whoseimplementation may differ from what is shown. The connections shown inFIG. 1 are logical connections; the actual physical connections may bedifferent. It is apparent to a person skilled in the art that the systemtypically comprises also other functions and structures than those shownin FIG. 1.

The embodiments are not, however, restricted to the system given as anexample but a person skilled in the art may apply the solution to othercommunication systems provided with necessary properties.

The example of FIG. 1 shows a part of an exemplifying radio accessnetwork.

FIG. 1 shows user devices 100 and 102 configured to be in a wirelessconnection on one or more communication channels in a cell with anaccess node (such as (e/g)NodeB) 104 providing the cell (and possiblyalso one or more other cells). The cells may be equally called sectors,especially when multiple cells are associated with a single access node(e.g., in tri-sector or six-sector deployment). Each cell may define acoverage area or a service area of the access node. Each cell may be,for example, a macro cell or an indoor/outdoor small cell (a micro,femto, or a pico cell). The physical link from a user device to a(e/g)NodeB is called uplink or reverse link and the physical link fromthe (e/g)NodeB to the user device is called downlink or forward link. Itshould be appreciated that (e/g)NodeBs or their functionalities may beimplemented by using any node, host, server or access point etc. entitysuitable for such a usage.

A communications system typically comprises more than one (e/g)NodeB inwhich case the (e/g)NodeBs may also be configured to communicate withone another over links, wired or wireless, designed for the purpose.These links may be used for signaling purposes. The (e/g)NodeB is acomputing device configured to control the radio resources ofcommunication system it is coupled to. The NodeB may also be referred toas a base station, an access point or any other type of interfacingdevice including a relay station capable of operating in a wirelessenvironment. The (e/g)NodeB includes or is coupled to transceivers. Fromthe transceivers of the (e/g)NodeB, a connection is provided to anantenna unit that establishes bi-directional radio links to userdevices. The antenna unit may comprise a plurality of antennas orantenna elements. The (e/g)NodeB is further connected to core network110 (CN or next generation core NGC). Depending on the system, thecounterpart on the CN side can be a serving gateway (S-GW, routing andforwarding user data packets), packet data network gateway (P-GW), forproviding connectivity of user devices (UEs) to external packet datanetworks, or mobile management entity (MME), etc.

The user device (also called UE, user equipment, user terminal, terminaldevice, etc.) illustrates one type of an apparatus to which resources onthe air interface are allocated and assigned, and thus any featuredescribed herein with a user device may be implemented with acorresponding apparatus, such as a relay node. An example of such arelay node is a layer 3 relay (self-backhauling relay) towards the basestation.

The user device typically refers to a portable computing device thatincludes wireless mobile communication devices operating with or withouta subscriber identification module (SIM), including, but not limited to,the following types of devices: a mobile station (mobile phone),smartphone, personal digital assistant (PDA), handset, device using awireless modem (alarm or measurement device, etc.), laptop and/or touchscreen computer, tablet, game console, notebook, and multimedia device.Each user device may comprise one or more antennas. It should beappreciated that a user device may also be a nearly exclusive uplinkonly device, of which an example is a camera or video camera loadingimages or video clips to a network. A user device may also be a devicehaving capability to operate in (Industrial) Internet of Things ((I)IoT)network which is a scenario in which objects are provided with theability to transfer data over a network without requiring human-to-humanor human-to-computer interaction. The user device (or in someembodiments a layer 3 relay node) is configured to perform one or moreof user equipment functionalities. The user device may also be called asubscriber unit, mobile station, remote terminal, access terminal, userterminal or user equipment (UE) just to mention but a few names orapparatuses.

The exemplifying radio access network of FIG. 1 may also comprise one ormore (dedicated) IoT or IIoT devices (not shown in FIG. 1) which areable to communicate with the access node 104 only via one or more of theuser devices 100, 102 (i.e., they are unable to communicate directlywith the access node 104).

Various techniques described herein may also be applied to acyber-physical system (CPS) (a system of collaborating computationalelements controlling physical entities). CPS may enable theimplementation and exploitation of massive amounts of interconnected ICTdevices (sensors, actuators, processors microcontrollers, etc.) embeddedin physical objects at different locations. Mobile cyber physicalsystems, in which the physical system in question has inherent mobility,are a subcategory of cyber-physical systems. Examples of mobile physicalsystems include mobile robotics and electronics transported by humans oranimals.

Additionally, although the apparatuses have been depicted as singleentities, different units, processors and/or memory units (not all shownin FIG. 1) may be implemented.

5G enables using (massive) multiple input-multiple output ((m)MIMO)antennas (each of which may comprise multiple antenna elements), manymore base stations or nodes than the LTE (a so-called small cellconcept), including macro sites operating in co-operation with smallerstations and employing a variety of radio technologies depending onservice needs, use cases and/or spectrum available. A MIMO antenna(comprising a plurality of antenna elements) may be equally called aMIMO array antenna or a MIMO antenna array (comprising a plurality ofantennas). 5G mobile communications supports a wide range of use casesand related applications including video streaming, augmented reality,different ways of data sharing and various forms of machine typeapplications, including vehicular safety, different sensors andreal-time control. 5G is expected to have multiple radio interfaces,namely below 6 GHz, cmWave and mmWave, and also being integratable withexisting legacy radio access technologies, such as the LTE. Integrationwith the LTE may be implemented, at least in the early phase, as asystem, where macro coverage is provided by the LTE and 5G radiointerface access comes from small cells by aggregation to the LTE. Inother words, 5G is planned to support both inter-RAT operability (suchas LTE-5G) and inter-RI operability (inter-radio interface operability,such as below 6 GHz-cmWave, below 6 GHz-cmWave-mmWave). One of theconcepts considered to be used in 5G networks is network slicing inwhich multiple independent and dedicated virtual sub-networks (networkinstances) may be created within the same infrastructure to run servicesthat have different requirements on latency, reliability, throughput andmobility.

The current architecture in LTE networks is fully distributed in theradio and fully centralized in the core network. The low latencyapplications and services in 5G require to bring the content close tothe radio which leads to local break out and multi-access edge computing(MEC). 5G enables analytics and knowledge generation to occur at thesource of the data. This approach requires leveraging resources that maynot be continuously connected to a network such as laptops, smartphones,tablets and sensors. MEC provides a distributed computing environmentfor application and service hosting. It also has the ability to storeand process content in close proximity to cellular subscribers forfaster response time. Edge computing covers a wide range of technologiessuch as wireless sensor networks, mobile data acquisition, mobilesignature analysis, cooperative distributed peer-to-peer ad hocnetworking and processing also classifiable as local cloud/fog computingand grid/mesh computing, dew computing, mobile edge computing, cloudlet,distributed data storage and retrieval, autonomic self-healing networks,remote cloud services, augmented and virtual reality, data caching,Internet of Things (massive connectivity and/or latency critical),critical communications (autonomous vehicles, traffic safety, real-timeanalytics, time-critical control, healthcare applications).

The communication system is also able to communicate with othernetworks, such as a public switched telephone network or the Internet112, or utilize services provided by them. The communication network mayalso be able to support the usage of cloud services, for example atleast part of core network operations may be carried out as a cloudservice (this is depicted in FIG. 1 by “cloud” 114). The communicationsystem may also comprise a central control entity, or a like, providingfacilities for networks of different operators to cooperate for examplein spectrum sharing.

Edge cloud may be brought into radio access network (RAN) by utilizingnetwork function virtualization (NVF) and software defined networking(SDN). Using edge cloud may mean access node operations to be carriedout, at least partly, in a server, host or node operationally coupled toa remote radio head (also called as a remote radio unit) or base stationcomprising radio parts. It is also possible that node operations will bedistributed among a plurality of servers, nodes or hosts. Application ofcloudRAN architecture enables RAN real time functions being carried outat the RAN side (in a distributed unit, DU 104) and non-real timefunctions being carried out in a centralized manner (in a centralizedunit, CU 108).

It should also be understood that the distribution of labor between corenetwork operations and base station operations may differ from that ofthe LTE or even be non-existent. Some other technology advancementsprobably to be used are Big Data and all-IP, which may change the waynetworks are being constructed and managed. 5G (or new radio, NR)networks are being designed to support multiple hierarchies, where MECservers can be placed between the core and the base station or nodeB(gNB). It should be appreciated that MEC can be applied in 4G networksas well.

5G may also utilize satellite communication to enhance or complement thecoverage of 5G service, for example by providing backhauling. Possibleuse cases are providing service continuity for machine-to-machine (M2M)or Internet of Things (IoT) devices or for passengers on board ofvehicles, or ensuring service availability for critical communications,and future railway/maritime/aeronautical communications. Satellitecommunication may utilize geostationary earth orbit (GEO) satellitesystems, but also low earth orbit (LEO) satellite systems, in particularmega-constellations (systems in which hundreds of (nano)satellites aredeployed). Each satellite 106 in the mega-constellation may coverseveral satellite-enabled network entities that create on-ground cells.The on-ground cells may be created through an on-ground relay node 104or by a gNB located on-ground or in a satellite.

It is obvious for a person skilled in the art that the depicted systemis only an example of a part of a radio access system and in practice,the system may comprise a plurality of (e/g) NodeBs, the user device mayhave an access to a plurality of radio cells and the system may comprisealso other apparatuses, such as physical layer relay nodes or othernetwork elements, etc. At least one of the (e/g) NodeBs or may be a Home(e/g) nodeB. Additionally, in a geographical area of a radiocommunication system a plurality of different kinds of radio cells aswell as a plurality of radio cells may be provided. Radio cells may bemacro cells (or umbrella cells) which are large cells, usually having adiameter of up to tens of kilometers, or smaller cells such as micro-,femto- or picocells. The (e/g)NodeBs of FIG. 1 may provide any kind ofthese cells. A cellular radio system may be implemented as a multilayernetwork including several kinds of cells. Typically, in multilayernetworks, one access node provides one kind of a cell or cells, and thusa plurality of (e/g)NodeBs are required to provide such a networkstructure.

For fulfilling the need for improving the deployment and performance ofcommunication systems, the concept of “plug-and-play” (e/g)NodeBs hasbeen introduced. Typically, a network which is able to use“plug-and-play” (e/g)Node Bs, includes, in addition to Home (e/g)NodeBs(H(e/g)nodeBs), a home node B gateway, or HNB-GW (not shown in FIG. 1).A HNB Gateway (HNB-GW), which is typically installed within anoperator's network may aggregate traffic from a large number of HNBsback to a core network.

The 5G massive MIMO systems as described above require solutions forprocessing data for a large number of antenna elements so as to performbeamforming efficiently and effectively. These schemes are essential forobtaining high gain with massive MIMO systems. Ideally, the beamformingschemes should be such that high system performance (e.g., spectralefficiency) is obtained without excessive implementation complexity. Theperformance of the beamforming scheme depends on the used algorithm aswell as on the type and amount of information required by saidalgorithm. Typically in 5G, the required information is obtained byreports sent by terminal devices and/or is based on sounding referencesignal (SRS) estimation in uplink. The sounding reference signal is areference signal transmitted by the terminal device in the uplinkdirection (i.e., to the access node) which may be used for estimatingthe uplink channel quality over a wide bandwidth. Furthermore, often themore advanced the beamforming schemes require as input more channelstate information (CSI) and, as a consequence, such advanced beamformingscheme can often be quite sensitive to estimation errors. Also, thecomputational complexity often becomes a problem when more advancedbeamforming schemes employing large amounts of CSI are used. Typically,the solutions require matrix operations which have computationalcomplexity of O(n³). As the size of the required matrices and theirnumber increases, the computational complexity may easily become toohigh for practical systems.

Well-known beamforming schemes include Grid-of-Beams (GoB),eigenbeamforming (EBB) and various Zero Forcing (ZF) schemes. Inaddition to the algorithms themselves being different, theaforementioned beamforming schemes differ in regard to the inputinformation that is required by them. Typically, the GoB solutions arestatic (i.e., use only first order statistics), the EBB solutionsoperate using second order statistics and ZF solutions (and any variantsthereof) use full or perfect channel state information (CSI). Full orperfect CSI corresponds to complete knowledge of the ideal channelresponse. Full or perfect CSI is typically not available outsidesimulations. From the aforementioned alternatives, the Zero Forcingschemes have the largest potential performance provided that full CSI(i.e., accurate channel matrix) is available. However, the problem withsaid schemes lies with obtaining high quality full CSI, e.g., usingsounding reference signals (SRS), especially in interference limitedscenarios and far from the cell edge. High quality (up-to-date) full CSIcan be rather hard to achieve also due to the delay between channelestimation and applying the beamforming weights. High quality full CSIcan often be achieved if the users (i.e., terminal devices) are static(i.e., not moving) though achieving high quality full CSI with movingusers, especially users having moderate-to-high velocity, is often notfeasible. Another potential problem is the high computational complexityrequired.

The solutions according to embodiments to be discussed below seek toimprove limitations of the earlier beamforming schemes by performingbeamforming in a distributed MIMO scenario, using a partitioned schemewhere first, an eigenbeamforming is performed, for each individual(remote) radio unit, based on second order statistics and, second, asingle-user MIMO optimization is performed between the remote radio unitfor each terminal device. Optionally, in the first part, an interferenceaware eigenbeamforming scheme may be used for further improving theperformance.

As embodiments relate to eigenbeamforming, the eigenbeamforming (andbeamforming in general) is discussed here in brief in order tofacilitate the discussion of the embodiments. In conventional(eigen)beamforming, the following linear channel model for a transmitter(e.g., an access node) and a single receiver (e.g., a single terminaldevice or, here specifically, the kth terminal device of a plurality ofterminal devices) is considered:y _(k) =H _(k) t _(k) x _(k) +n,where H_(k) is a channel matrix of the radio channel for the kthterminal device, t_(k) is a pre-coding vector for the kth terminaldevice defining a set of beamforming weights, y_(k) is a received signal(vector) for the kth terminal device before decoding, x_(k) is atransmit signal for the kth terminal device (i.e., the transmittedsymbol) and n is an additive receiver noise vector. Each element of theadditive receiver noise vector n may be assumed to have zero mean andvariance σ². The received signal y_(k) is a vector which is decoded(e.g., by linearly combining its elements) by the receiver so as to forma received symbol y_(k). The precoding vector t_(k) serves to adjust thephases and/or amplitudes of the transmitted signal (i.e., transmittedsymbols) as it is transmitted via a plurality of antennas. Based on thesuperposition principle of electromagnetic waves, this results inconstructive interference for some radiation directions and destructiveinterference for other radiation directions and thus a specifictransmission radiation pattern (or a specific beam) is formed. Theelements of the precoding vector t_(k) are called beamforming weights(or equally beamforming coefficients). Any of the quantities mentionedabove (y_(k), H_(k), t_(k), x_(k) and n) may be complex-valued. Thetransmit power may be included in the pre-coding vectors t_(k) (i.e.,the pre-coding vectors are not necessarily unit vectors). In otherwords, transmit power P_(k) associated with a particular pre-codingvector t_(k) may be defined as ∥t_(k)∥²=P_(k) with ∥ . . . ∥corresponding to norm or specifically Euclidean norm.

In eigenbeamforming, the beamforming weights of the pre-coding vectorare optimized by analyzing the channel covariance matrix R=E(H^(H)H) ofthe radio channel (where H is a channel matrix, H denotes the conjugatetranspose operation and E denotes an expected value operation). Thechannel covariance matrix describes the macroscopic effects, includingspatial channel correlation and average pathloss in different spatialdirections. It is a well-known result that channel capacity of the radiochannel is optimized when the beamforming weights are chosen to be equalto the eigenvectors of the channel covariance matrix. Channel capacityis a measure of maximal transmission rate such that arbitrarily smalldecoding error rate can be achieved. Thus, in eigenbeamforming, thebeamforming problem becomes a problem of finding eigenvalues andeigenvectors of the channel covariance matrix. In practice, thebeamforming weights are typically determined from the eigenvaluedecomposition of the channel covariance matrix.

One example of a conventional eigenbeamforming using second orderstatistics is discussed as a special case of the interference awareeigenbeamforming scheme in relation to FIGS. 4A and 4B.

The eigenbeamforming scheme as described above may be used for formingbeams for transmission to a plurality of terminal devices. However, thebasic eigenbeamforming scheme does not take into account interferencecaused by the transmission using multiple beams. Obviously, if a firstbeam is used for transmission from an access node to a first terminaldevice and a second beam is used simultaneously for transmission fromthe access node to a second terminal device, the first terminal device(if located near the second terminal device) also receives the secondsignal and vice versa. This causes interference in the receptiondeteriorating the performance. Some of the embodiments seek to improveupon the conventional eigenbeamforming approach, in this regard, byintroducing interference awareness to the conventional eigenbeamforming(to be discussed in detail below).

FIG. 2 illustrates another example of a communications system 200 towhich some embodiments may be applied. The communications system 200 maycorrespond the communication system as discussed in relation to FIG. 1or a part thereof. Therefore, any of the terminal devices 221, 222, 223,224 may correspond to either of elements 100, 102 of FIG. 1. Moreover,the access node 104 of FIG. 1 may correspond to a combination of theelements 201, 202, 203, 220 forming a distributed access node. Theillustrated communications system may be based on New Radio (NR) accesstechnology.

Referring to FIG. 2, a communication system 200 comprises three (remote)radio units 201, 202, 203 providing respective (neighboring) cells 211,212, 213, a distributed unit 220 connected to each of the remote radiounits 201, 202, 203 via wired and/or wireless communications links and acentralized unit 230 connected to the distributed unit 220 via a wiredor wireless communications link. Each of the elements 201, 202, 203,220, 230 may be associated with the same access node (e.g., the samegNB). Each remote radio unit 201, 202, 203 may be MIMO-capable (i.e.,comprise a MIMO antenna array and associated signal processing means forperforming beamforming using said MIMO antenna array). Moreover, thecommunication system 200 comprises a plurality of terminal devices 221,222, 223, 224 located within said cells 211, 212, 213. In otherembodiments, the number of the remote radio units may be differentcompared to the illustrated example though to fully benefit from thedistributed architecture, the access node should comprise at least tworemote radio units. While FIG. 2 illustrates only a single distributedunit 220 for simplicity, in other embodiments two or more distributedunits 220 connected to the same centralized unit 230 may be provided.

The communications system 200 specifically corresponds to a distributedcommunication system, more specifically to a distributed MIMOcommunication scenario. Distributed MIMO may be equally calledcooperative MIMO, network MIMO, virtual MIMO or virtual antenna arrays.In distributed MIMO, a plurality of distributed antennas (or antennaarrays or panels) on different radio devices are employed to achieveimproved performance in terms of gain (even close to theoretical limitsof MIMO). The basic idea of distributed MIMO is to group multipledevices into a virtual antenna array to achieve MIMO communications.

Even more specifically, the illustrated communication system 200 may beconfigured to employ coordinated multipoint (CoMP) which is one specifictype of distributed MIMO. In CoMP, data and channel state information(CSI) is shared among neighboring access points (here, remote radiounits 201, 202, 203) to coordinate their transmissions in the downlinkand jointly process the received signals in the uplink. The embodimentsare specifically related to coordinating transmissions in downlink andthus the uplink operation may be considered optional in view of theembodiments. The basic idea in CoMP techniques is employing theotherwise harmful inter-cell interference into useful signals, enablingimprovements in power gain, channel rank, and/or diversity gain.

In CoMP and in distributed MIMO in general, very-low latency exchange ofinformation (e.g., data, control information, and CSI) between theaccess points 201, 202, 203 is required. For example, the informationneeded for scheduling may need to be available at each coordinatedaccess point in the order of a millisecond. This low-latency informationsharing may be arranged in multiple different ways. As an example, FIG.2 illustrates a centralized solution where a distributed unit 220capable of communication with each of the remote radio units 201, 202,203 is provided. The distributed unit 220 may be co-located with one ofthe radio units 201, 202, 203 and/or with the centralized unit 230. Theremote radio units 201, 202, 203 may be interconnected via thedistributed unit 220 with low latency communication links in order toexchange information. The connection between the centralized unit 220and the access nodes 201, 202, 203 may be provided via wired and/orwireless communications links. For example, optical fiber links may beemployed.

FIG. 3 illustrates a process according to embodiments for performingbeamforming optimization according to embodiments. The illustratedprocess of FIG. 3 may be performed by an apparatus (or computing device)for performing beamforming optimization (i.e., for calculating optimalbeamforming weights). Said apparatus may be an access node (e.g., theaccess node 104 of FIG. 1) or a part thereof. Said apparatus mayspecifically be a distributed unit of an access node such as thedistributed unit 220 of FIG. 2. It may be assumed that said distributedunit is connected electrically to two or more remote radio unitsenabling transmission to a plurality of terminal devices. Moreover, theplurality of terminal devices may be specifically configured (orscheduled) to use the same time and/or frequency resource(s) (i.e., thesame physical resource block or blocks) for reception from the accessnode.

Referring to FIG. 3, it is initially assumed, in block 301, that theapparatus maintains, in a database, channel state information (CSI) of aplurality of radio channels. Each of the plurality of radio channels isdefined to be between one of two or more remote radio units of adistributed access node and one of a plurality of terminal devices. Theplurality of radio channels may encompass all combinations of a terminaldevice of the plurality of terminal devices and a remote radio unit ofthe two or more remote radio units. The channel state informationcomprises at least first and second order statistics of the plurality ofradio channels. The plurality of terminal devices may be specificallyconfigured (or scheduled) to use the same time and/or frequencyresource(s) (i.e., the same physical resource block or blocks) forreception from the access node. The database may be an internal orexternal database of the apparatus. The CSI may comprise one or more(current and/or historical) channel matrices for each of the pluralityof radio channels. In view of the following discussion, the pluralityterminal devices may be denoted by indices k=1, 2, . . . , N, where N isa positive integer larger than one indicating the number of theplurality of terminal devices. Sometimes, index i is used instead of k.

First order statistics of a radio channel only capture the staticbehavior of the radio channel (i.e., they describe an arithmetic mean ofa data set). On the other hand, second order statistics of a radiochannel are able to capture the correlation properties of the radiochannel (i.e., they describe a variance of a data set with respect tothe arithmetic mean or, when matrices are considered, a covariancematrix of a matrix corresponding to the data set) and are thus able toprovide a dynamic representation of the system performance. In otherwords, the first order statistics correspond to a first moment of a dataset while the second order statistics correspond to a second moment of adata set.

In some embodiments, the first order statistics of the plurality ofradio channels may comprise, for each of the plurality of radiochannels, at least a (short-term) channel matrix H_(k).

The CSI maintained in the database may have been acquired and/orcalculated based on, e.g., the SRS measurements performed by the accessnode with each of the plurality of terminal devices and/or other radiomeasurements (e.g., timing advance, time of arrival and/or pathlossmeasurements) carried out between the access node and the plurality ofterminal devices. The CSI maintained in the database may be updatedregularly as new radio measurements are carried out.

The apparatus calculates, in block 302, separately for each of the twoor more remote radio units, first sets of beamforming weights forforming beams for transmitting from a corresponding remote radio unit toeach of a plurality of terminal devices based on the second orderstatistics (i.e., long-term CSI) associated with the correspondingremote radio unit using an eigenbeamforming scheme. In other words, afirst set of beamforming weights may be calculated for each combinationof a remote radio unit of the two or more remote radio units and aterminal device of the plurality of terminal device. The beamformingusing the beamforming scheme in block 302 may comprise, for each remoteradio unit, performing optimization to minimize total transmit power fortransmission from the remote radio unit to the plurality of terminaldevices subject to a pre-defined constraint on a minimum allowableexpected value of signal-to-interference-plus-noise ratio (SINR) or ofsignal-to-noise ratio (SNR) for the plurality of the terminal devices.In the optimization, the total transmit power may be defined based onsets of beamforming weights used for forming beams for transmitting tothe plurality of terminal devices and the pre-defined constraint may beevaluated, in the optimization for each of the plurality of terminaldevices, against expected values of SINR for a terminal devicecalculated based on the second order statistics for the terminal device(i.e., for the radio channel between the access node and the terminaldevice) and sets of beamforming weights for the plurality of terminaldevices.

The eigenbeamforming scheme used in block 302 may be any beamformingscheme based on the eigenbeamforming principle. Specifically, theeigenbeamforming scheme may be a conventional eigenbeamforming schemewhich does not take into account multi-user interference or aninterference aware eigenbeamforming scheme (or any other advancedeigenbeamforming scheme). In the former case, SNR may be evaluated whilein the latter case SINR may be employed instead. The interference awareeigenbeamforming scheme according to embodiments (and also brieflyeigenbeamforming without taking interference into account) is discussedin detail in relation to FIGS. 4A, 4B and 5.

The apparatus performs, in block 303, for each terminal device of theplurality of terminal devices, single-user MIMO optimization between thetwo or more remote radio units at least to maximize a pre-defined metricbased on all first sets of beamforming weights associated withtransmission from the two or more remote radio units to a correspondingterminal device and on the first order statistics (i.e., short-term CSI)of radio channels between each of the two or more remote radio units andthe corresponding terminal device. The result of the single-user MIMOoptimization, for each terminal device, is a second set of beamformingweights to be applied for transmission to said terminal device (at theassociated remote radio units). The pre-defined metric may be one of amutual information metric and signal-to-interference-plus-noise ratio(SINR). The mutual information metric may be any known mutualinformation metric such as Mean Mutual Information per coded Bit (MMIB).

In the single-user MIMO optimization, a signal y_(k) received at the kthterminal device of the plurality of terminal devices may be modelled,as:y _(k) ={tilde over (H)} _(k) T _(k) W _(k) x _(k) +n,wherein {tilde over (H)}_(k) is a combined channel matrix for theplurality of terminal devices and the two or more remote radio unitsdefined as {tilde over (H)}_(k)=[H_(k) ⁽¹⁾, . . . , H_(k) ^((M))] withH_(k) ^((m)) being the channel matrix for the kth terminal device andmth remote radio unit and M being the number of the two or more remoteradio units, T_(k)=[t_(k) ⁽¹⁾; . . . ; t_(k) ^((M))] with t_(k) ^((m))being a pre-coding vector (a column vector) for the kth terminal deviceand mth remote radio unit defining a first set of beamforming weights,W_(k) is a second pre-coding vector for the kth terminal device defininga second set of beamforming weights, x_(k) is a transmit signal for thekth terminal device and n is an additive receiver noise vector. In otherwords, the matrix {tilde over (H)}_(k) contains the plurality of channelmatrices associated with each of the two or more remote radio unitscollected row-wise while the matrix T_(k) contains the beamformingweights associated with each of the two or more remote radio units (andcalculated based on second order statistics) stacked column-wise.

In some embodiments, the performing of the single-user MIMO optimizationcomprises, for each terminal device of the plurality of terminaldevices, calculating the second set of beamforming weights W_(k,opt)specifically as

$W_{k,{opt}} = {\underset{W_{k}}{argmax}{{\log( {\det( {I + {{\overset{\sim}{H}}_{k}T_{k}W_{k}W_{k}^{H}T_{k}^{H}{\overset{\sim}{H}}_{k}^{H}}} )} )}.}}$Here, log(det(I+{tilde over (H)}_(k) T_(k)W_(k)W_(k) ^(H)T_(k)^(H){tilde over (H)}_(k) ^(H))) is the mutual information metric(mentioned above) and det denotes a determinant operation. The aboveequation may be written equally as

$\begin{matrix}{W_{k,{opt}} = {\arg\;{\max\limits_{W_{k}}{\log( {\det( {I + {T_{k}^{H}{\overset{\sim}{H}}_{k}^{H}{\overset{\sim}{H}}_{k}T_{k}W_{k}W_{k}^{H}}} )} )}}}} \\{= {\arg\;{\max\limits_{W_{k}}{{\log( {\det( {I + {V_{k}\Lambda_{k}V_{k}^{H}W_{k}W_{k}^{H}}} )} )}.}}}}\end{matrix}$

In the last equation, an eigenvalue decomposition (or equallyeigendecomposition) of T_(k) ^(H){tilde over (H)}_(k) ^(H){tilde over(H)}_(k)T_(k) has been carried out, where V_(k) is a unitary matrixdefining the eigenvectors of the matrix T_(k) ^(H){tilde over (H)}_(k)^(H){tilde over (H)}_(k) T_(k) and Λ_(k) is a diagonal matrix defined asΛ_(k)=diag(λ₁, . . . , λ_(n)), where λ₁, . . . , λ_(n), are eigenvaluesof the matrix T_(k) ^(H){tilde over (H)}_(k) ^(H){tilde over(H)}_(k)T_(k). Thus, it is easy to see, from said last equation, thatthe beamforming weights (i.e., the beam) is optimized when eigenvectorsV_(k) corresponding to the largest eigenvalues Λ_(k) are chosen as thepre-coding vectors in the second set.

The optimization described in the previous paragraph correspond to rateoptimization to maximize mutual information. As mentioned above, inother embodiments, SINR may be optimized (or specifically maximized)instead of the mutual information metric. Moreover, the apparatus mayfurther perform, also in block 303, power optimization. The poweroptimization may be based on, for example, the water filling principle(or equally water filling algorithm) or an equal gain scheme (or equalgain allocation).

After the single-user optimization has been performed for each of theplurality of terminal devices in block 303, the apparatus causestransmitting, in block 304, data, from the two or more remote radiounits to the plurality of terminal devices, using beams formed byapplying both first and second sets of optimized beamforming weights atthe two or more remote radio units. Specifically, the first and secondset of beamforming weights may be applied according to the modely_(k)={tilde over (H)}_(k)T_(k)W_(k)x_(k)+n described above. The causingtransmitting of data in block 304 may comprise transmitting, by theapparatus being a distributed unit of an access node, information on theresults of the optimization (i.e., first and second sets of optimizedbeamforming weights) to the two or more remote radio units forperforming beamforming (by said two or more remote radio units). Eachremote radio unit transmits, in response to receiving said results ofthe optimization, data using one or more beams formed according to thefirst and second sets of optimized beamforming weights to the pluralityof terminal devices. Obviously, only the first and second sets ofbeamforming weights which are to be used by a particular remote radiounit need to be transmitted to that remote radio unit.

In the beamforming optimization according to embodiments discussedabove, the co-operation between separate remote radio units must beimplemented using first order statistics in order to guarantee thestability of the antenna response. This requires the scheme to befrequency selective similar to Zero Forcing schemes. The advantage ofthe proposed scheme according to embodiments is that related matrixsizes are considerably smaller compared to Zero Forcing-based solutions.As the number of matrix manipulations typically scales with the matrixorder as O(n³), the solution according to embodiments provides animprovement in computational complexity compared to prior solutions.Also, as the number of estimated parameters is reduced, added robustnessagainst estimation errors is also provided.

In the following, the interference aware eigenbeamforming which isemployed in some embodiments for performing the remote radiounit-specific optimization (i.e., actions pertaining to block 302) isdescribed in detail in connection with FIGS. 4A, 4B and 5. It should benoted that upper indices (1), (2), . . . , (M) used with H_(k) and t_(k)for denoting different remote radio units above is not used in relationto FIGS. 4A, 4B and 5 for simplicity of notations (and since theoptimization described in relation to said Figures is performedseparately for each remote radio unit and thus there is no need todistinguish between different remote radio units).

FIG. 4A illustrates a process according to embodiments for performingbeamforming using an interference aware eigenbeamforming schemeaccording to embodiments. The illustrated process of FIG. 4A may beperformed by an apparatus (or computing device) for performingbeamforming optimization (i.e., for calculating optimal beamformingweights). Said apparatus may be specifically a distributed unit of adistributed access node (e.g., the distributed unit 220 of FIG. 2). Itis assumed that the apparatus is connected electrically (e.g., via anoptical fiber connection) to two or more remote radio units of thedistributed access node.

The process illustrated in FIG. 4A may correspond to block 302 of FIG.3. Therefore, it is assumed that the apparatus, initially, maintainschannel state information (CSI) of a plurality of radio channels betweentwo or more distributed radio units and a plurality of terminal devicesin a database. The channel state information maintained in the databaseis assumed to comprise at least (first and) second order statistics ofthe plurality of radio channels.

For each remote radio unit of the two or more remote radio units, theapparatus performs, in block 401, optimization to minimize totaltransmit power for transmission from a corresponding remote radio unitto the plurality of terminal devices subject to a pre-defined constrainton a minimum allowable expected value ofsignal-to-interference-plus-noise ratio (SINR) for the plurality of theterminal devices.

In the optimization in block 401, the total transmit power is definedbased on sets of beamforming weights used for forming beams fortransmitting to the plurality of terminal devices. Specifically, thetotal transmit power may be defined as a sum of squares of (Euclidean)norms of pre-coding vectors defined for the plurality of terminaldevices. A pre-coding vector for a given terminal device comprises a setof beamforming weights for forming a beam for transmitting (from acorresponding remote radio unit) to said terminal device. Thus, theresult of the optimization is the total transmit power as well as thesets of (optimal) beamforming weights for the plurality of terminaldevice (or equally pre-coding vectors for the plurality of terminaldevices). Each pre-coding vector for a terminal device may be dependenton the transmit power allocated for said terminal device and a set ofnormalized beamforming weights (i.e., forming a unit vector).

Moreover, the pre-defined constraint is evaluated, in the optimizationin block 401 for each of the plurality of terminal devices, bycalculating expected values of SINR for a terminal device based onsecond order statistics (e.g., channel covariance matrices) for theterminal device (i.e., for the radio channel between the access node andthe terminal device) and sets of beamforming weights for the pluralityof terminal devices. Further, information on noise at the receiver(i.e., additive receiver noise) may be employed in the calculation ofthe SINR. Specifically, the desired signal part of the SINR, for aterminal device, may be calculated based on the second order statistics(e.g., a channel covariance matrix) for said terminal device and on aset of beamforming weights for said terminal device while theinterference part of the SINR may be calculated based on the secondorder statistics (e.g., channel covariance matrices) for the terminaldevice and on the set of beamforming weights for the plurality ofterminal devices excluding said terminal device.

The first set of optimized beamforming weights, for each of the two ormore remote radio units, resulting from the optimization in block 401may be specifically the set of beamforming weights corresponding to theminimized total transmit power (that is, minimized subject to thepre-defined constraint) for transmission from a corresponding remoteradio unit to the plurality of terminal devices.

It should be noted that the full solution to the beamforming problem issolved typically by means of an iterative process. First, a set of powervalues for the plurality of terminal devices may be defined andcorresponding sets of beamforming weights may be optimized. Thereafterbased on the SINR calculated for each terminal device, the power valuesmay be modified and subsequently the process may be repeated with theupdated power values. These steps may be repeated until certainpre-defined conditions (for the SINR) have been satisfied.

In some embodiments, the transmit power allocated for each terminaldevice of the plurality of terminal devices may be pre-defined. Thepower may be distributed between the plurality of terminal devices,e.g., based on pathloss and/or spatial correlation.

It should be emphasized that the optimization in block 401 is performedspecifically based on said second order statistics of the plurality ofradio channels (maintained in the database) taking into account, incontrast to the linear channel model discussed in relation toconventional eigenbeamforming, also interference resulting fromtransmission using multiple beams, i.e., inter-stream interference (asis evident also from the fact that SINR is considered in theoptimization).As interference is taken into account in the optimizationin block 401, the optimization, for each remote radio unit, iseffectively based on the following linear channel model:

${y_{k} = {{H_{k}t_{k}x_{k}} + {\sum\limits_{i \neq k}{H_{k}t_{i}x_{i}}} + n}},$

where y_(k) is a received signal (vector) at the kth terminal device ofthe plurality of terminal devices, as H_(k) is a channel matrix for thekth terminal device, t_(k) is a pre-coding vector for the kth terminaldevice defining a set of beamforming weights, x_(k) is a transmittedsignal (or symbol) for the kth terminal device, n is additive receivernoise vector (where each element may have zero mean and variance σ²) anda sum of Σ_(i≠k)H_(k)t_(i)x_(i) is calculated over all but one of theplurality of terminal devices. Said sum of Σ_(i≠k)H_(k)t_(i)x_(i)corresponds to (multiuser) interference resulting from simultaneoustransmissions to other terminal devices using corresponding other beams.Preferably, the pre-coding vectors of the plurality of terminal devicesshould be selected such that these interference terms are minimized. Itshould be noted that the above equation may be equally written as:

${y_{k} = {{\sum\limits_{i}{H_{k}t_{i}x_{i}}} + n}},$where the sum is calculated over all of the plurality of terminaldevices (i.e., over i=1, . . . , N). As mentioned above, the transmitpower may be included in the pre-coding vectors t_(k) (i.e., thepre-coding vectors are not necessarily unit vectors). In other words,transmit power P_(k) associated with a particular pre-coding vectort_(k) may be defined as ∥t_(k)∥²=P_(k).

The performing of the optimization in block 401 may comprisespecifically solving, for each remote radio unit, an optimizationproblem formulated, using the notation introduced in the previousparagraph, as:

$\min\limits_{i}{\sum\limits_{i}{t_{i}}^{2}}$

subject to

${\gamma \leq {\frac{t_{k}^{H}R_{k}t_{k}}{{\sum\limits_{i \neq k}{t_{i}^{H}R_{k}t_{i}}} + \delta^{2}}\mspace{14mu}{for}\mspace{14mu}{all}\mspace{14mu} k}},$

where i and k are indices indicating the ith and kth terminal device ofthe plurality of terminal device, t_(i) is a pre-coding vector for theith terminal device defining a set of beamforming weights, γ is theminimum allowable expected value of SINR (of the pre-definedconstraint), δ² is a noise term (which may be equal to noise varianceσ²), R_(k) is a channel covariance matrix E(H_(k) ^(H) H_(k)) with H_(k)being a complex non-deterministic channel matrix for the kth terminaldevice, E denoting an expected value and H denoting a conjugatetranspose operation. Further, the sum of Σ_(i≠k)t_(i) ^(H) R_(k)t_(i) iscalculated over all but one of the plurality of terminal devices, t_(k)^(H)R_(k)t_(k) corresponds to a received desired signal power for thekth terminal device and Σ_(i≠k)t_(i) ^(H) R_(k)t_(i) corresponds to atotal received interference power for the kth terminal device. The termΣi∥t_(i)∥² corresponds to the total transmit power.

In some embodiments, the solving of the optimization problem for eachremote radio unit described above in relation block 401 comprisessolving an equivalent (eigenvalue) problem defined through the equation(defined here for the kth terminal device of the plurality of terminaldevices):

${{( {I + {\sum\limits_{i}{\frac{\lambda_{i}}{\delta^{2}}R_{i}}}} )^{- 1}R_{k}t_{k}} = {\frac{\delta^{2}}{\lambda_{k}}( \frac{\gamma}{\gamma + 1} )t_{k}}},$

where I is an identity matrix, λ_(i) is a Lagrangian multiplier for theith terminal device relating to total transmit power P throughΣ_(i)λ_(i)=Σ_(i)∥t_(i)∥²=P at optimal solution (∥ . . . ∥ correspondingto norm or specifically Euclidean norm). Specifically, the optimalbeamforming weights for the plurality of terminal devices t_(k) (fork=1, 2, . . . , N) are found as corresponding eigenvectors of the aboveequation. A proof for the equivalency of the original optimizationproblem and the equivalent problem is provided following the discussionon the solving the equivalent problem.

In some embodiments, the Lagrangian multiplier λ_(i), for all i (i.e.,for all of the plurality of terminal devices), may have a pre-definedvalue. Said pre-defined value may or may not be different for differenti indices. In some embodiments, the Lagrangian multiplier λ_(i) may havethe same value for all i. This definition would guarantee fairness ofpower allocation between terminal devices.

In other embodiments, the Lagrangian multiplier λ_(i), for all i (i.e.,for all of the plurality of terminal devices) may not have a pre-definedvalue. In such cases, the values of the Lagrangian multiplier λ_(i) aredetermined through iteration during the optimization process.

Specifically, the performing of the optimization in block 401 maycomprise performing, by the apparatus, a process as illustrated in FIG.4B. The illustrated process is based on solving the equivalent problemdefined above.

Referring to FIG. 4B, the apparatus may perform the following separatelyfor each remote radio unit of the two or more remote radio units.Initially, the apparatus calculates, in block 411, for each k indicatingthe kth terminal device of the plurality of terminal devices, a matrixdefined as

$( {I + {\sum\limits_{i}{\frac{\lambda_{i}}{\delta^{2}}R_{i}}}} )^{- 1}{R_{k}.}$The matrix inversion

$( {I + {\sum\limits_{i}{\frac{\lambda_{i}}{\delta^{2}}R_{i}}}} )^{- 1}$may be calculated only once to simplify the calculation. In other words,the calculation in block 211 may comprise effectively two steps: 1)calculating a matrix inversion

$( {I + {\sum\limits_{i}{\frac{\lambda_{i}}{\delta^{2}}R_{i}}}} )^{- 1}$and 2) multiplying the inverted matrix calculated in the first step witha matrix R_(k) separately for each terminal device of the plurality ofterminal devices (i.e., for each k with k=1, 2, . . . , N). Then, theapparatus finds, in block 412, for each k indicating the kth terminaldevice of the plurality of terminal devices, the largest eigenvalue

$( {I + {\sum\limits_{i}{\frac{\lambda_{i}}{\delta^{2}}R_{i}}}} )^{- 1}{R_{k}.}$Here, the largest eigenvalue for each index k corresponds to a minimumof the total transmit power (while also fulfilling the pre-definedconstraint). This property is evident from the equation for theequivalent problem provided above having a form similar to thewell-known equation Av=λv describing the fundamental connection betweenan eigenvalue λ and an eigenvector v of a matrix A. The finding of thelargest eigenvector in block 412 may be performed using any conventionalmethod such as using power iteration. Finally, the apparatus finds, inblock 213, for each largest eigenvalue, a corresponding eigenvector.Each eigenvector corresponds, here, to a set of optimal beamformingweights (that is, optimal in terms of the aforementioned optimizationproblem) for a terminal device of the plurality of terminal devices. Theeigenvectors corresponding to each eigenvalue may be found by solvingthe equation

${( {I + {\sum\limits_{i}{\frac{\lambda_{i}}{\delta^{2}}R_{i}}}} )^{- 1}R_{k}t_{k}} = {\lambda_{{eigen},k}t_{k}}$for all k (i.e., for all of the plurality of terminal devices), whereλ_(eigen,k) is the largest eigenvalue for the kth terminal device.

If we change perspective to a fixed power constraint Σ_(i)∥t_(i)∥²≤P andoptimize SINR for each terminal device of the plurality of terminaldevices, given the optimal SINR values γ_(k) for each terminal device(i.e., for each k), we also know the beams from the solution givenabove. That solution must fulfill also said fixed power constraint.Thus, by knowing the solution to the aforementioned optimization problemor to the equivalent eigenvalueproblem, a solution is also provided tothis alternative problem. In other words, if we optimize the SINRsubject to the fixed power constraint, the resulting beams have the sameshape (i.e., the derived optimal beamforming weights are the same) aswhen the aforementioned optimization problem or to the equivalenteigenvalueproblem is solved.

In the following, a few comments are provided regarding certainadvantages of the interference aware eigenbeamforming solution accordingto embodiments. Firstly, the derived algorithm is based on second orderstatistics and allows averaging over time and frequency. In other words,the solution is effectively static in nature. This improves theestimation accuracy of the required input. The beam derivation is alsoconstant over frequency for a given set of scheduled terminal devices.Thus, there is only one shared matrix inversion for all frequencyresources and set of scheduled terminal devices (i.e., the solutionneeds to be calculated only once). Finding the largest eigenvalues andthe corresponding eigenvectors for each of the plurality of terminaldevice is, then, a relatively simple operation with, e.g., using powermethod. As a comparison, the Zero Forcing scheme needs to be calculatedseparately for different frequency resources. As an example, a 100 MHzwide 5G carrier has 273 physical resource blocks (PRB). To get thefrequency selective ZF solutions the equations need to be solved 273times. If the scheduled terminal devices occupy the whole bandwidth, theproposed solution in the given example needs to be solved only once.

In the following, a proof for equivalency of the original optimizationproblem and the equivalent (eigenvalue) problem as described above isprovided for completeness. The starting point is the aforementionedoptimization problem formulated as:

$\min{\sum\limits_{i}{t_{i}}^{2}}$

subject to a (pre-defined) constraint

$\gamma \leq {\frac{t_{k}^{H}R_{k}t_{k}}{{\sum\limits_{i \neq k}{t_{i}^{H}R_{k}t_{i}}} + \delta^{2}}\mspace{14mu}{for}\mspace{14mu}{all}\mspace{14mu}{k.}}$The above constraint for y may be rewritten as

${\frac{1}{\gamma\delta^{2}}t_{k}^{H}R_{k}t_{k}} \geq {{\sum\limits_{i \neq k}{\frac{1}{\delta^{2}}t_{i}^{H}R_{k}t_{i}}} + {1.}}$Now, an additional vector variable a is introduced so that we have:

${\frac{1}{\gamma\delta^{2}}t_{k}^{H}aa^{H}t_{k}} \geq {{\sum\limits_{i \neq k}{\frac{1}{\delta^{2}}t_{i}^{H}aa^{H}t_{i}}} + 1}$witht _(k) ^(H) aa ^(H) t _(k) =t _(k) ^(H) R _(k) t _(k).Then, the pre-defined constraint may be written as

${\sqrt{\frac{1}{\gamma\delta^{2}}}{{Re}( {t_{k}^{H}aa^{H}t_{k}} )}} \geq \sqrt{{\sum\limits_{i \neq k}{\frac{1}{\delta^{2}}t_{i}^{H}R_{k}t_{i}}} + 1.}$

Notably, this is a second order cone program (SOCP) constraint whilet_(k) ^(H) aa^(H)t_(k)=t_(k) ^(H) R_(k)t_(k) is a corresponding equalityconstraint. The Slater's condition can be fulfilled and thus it followsthat the Karush-Kuhn-Tucker (KKT) conditions define the optimalsolution. Therefore, we write a Lagrangian function

(t_(k)) of the aforementioned pre-defined constraint:

${{J( t_{k} )} = {{\sum\limits_{k}{\frac{1}{\delta^{2}}t_{k}^{H}t_{k}}} + {\sum\limits_{k}{\lambda_{k}( {{\sum\limits_{i \neq k}{\frac{1}{\delta^{2}}t_{i}^{H}R_{k}t_{i}}} + 1 - {\frac{1}{\gamma\delta^{2}}t_{k}^{H}R_{k}t_{k}}} )}}}},$where λ_(k) is Lagrangian multiplier associated with kth SINR constraint(i.e., with kth terminal device). The dual function is min_(t) ₁_(, . . . , t) _(K)

(t_(k))=Σ_(k)λ_(k) and the strong duality implies that it equals to thetotal power Σ_(k)∥t_(k)∥² at the optimal solution. Exploiting thestationary KKT conditions which state that ∂

(t_(k))/∂_(k)=0 for k=1, . . . , K at the optimal solution, we write(note that the indices are manipulated to a different order)

$\frac{\partial{J( t_{k} )}}{\partial t_{k}} = {{t_{k} + ( {{\sum\limits_{i \neq k}{\frac{\lambda_{i}}{\delta^{2}}R_{i}t_{k}}} - {\frac{\lambda_{k}}{\gamma\delta^{2}}R_{k}t_{k}}} )} = {\quad{ 0\Leftrightarrow{( {1 + {\sum\limits_{i}{\frac{\lambda_{i}}{\delta^{2}}R_{i}t_{k}}}} )t_{k}}  = {\frac{\lambda_{k}}{\delta^{2}}( {1 + \frac{1}{\gamma}} )R_{k}{t_{k}.}}}}}$By further moving the terms around, we get as a final result:

${( {1 + {\sum\limits_{i}\frac{\lambda_{i}}{\delta^{2}R_{i}}}} )^{- 1}R_{k}t_{k}} = {\frac{\delta^{2}}{\lambda_{k}}( \frac{\gamma}{\gamma + 1} ){t_{k}.}}$

It should be noted that the proposed beamforming scheme as described inrelation to FIGS. 4A and 4B converges to conventional eigenbeamformingas the amount of interference (i.e., the term Σ_(i≠k)t_(i)^(H)R_(k)t_(i)) goes to zero or as signal-to-noise ratio approacheszero. Thus, the proposed beamforming scheme may be called InterferenceAware Eigenbeamforming.

As described above, the conventional eigenbeamforming (which does nottake into account interference) may be derived from the interferenceaware eigenbeamforming by assuming that there is no interference, i.e.,assuming that Σ_(i≠k)t_(i) ^(H) R_(k)t_(i)=0 for all k. In such a case,the SINR corresponds to SNR. As the embodiments are not limited to usinginterference aware eigenbeamforming but may, alternatively, use anyconventional eigenbeamforming schemes which ignore the interference, the(interference unaware) eigenbeamforming scheme derivable from theinterference aware eigenbeamforming is discussed here briefly in view ofthe above discussion for completeness. In general, the above discussionas well as the discussion in relation to FIG. 5 applies to theconventional eigenbeamforming with the additional assumption that theamount of interference is zero in all cases (i.e., for all terminaldevices). This means, for example, that the optimization problem can bewritten as:

$\min{\sum\limits_{i}{t_{i}}^{2}}$

subject to

${\gamma \leq {\frac{t_{k}^{H}R_{k}t_{k}}{\delta^{2}}\mspace{11mu}{for}\mspace{14mu}\text{all}\mspace{11mu} k}},$where the term t_(k) ^(H)R_(k)t_(k)/δ² corresponds to signal-to-noiseratio (SNR) and correspondingly y is a minimum allowable expected valueof SNR. Moreover, the equivalent eigenvalue problem may be writtensimply as

${R_{k}t_{k}} = {\frac{\delta^{2}\gamma_{k}}{\lambda_{k}}{t_{k}.}}$

FIG. 5 illustrates another process according to embodiments forperforming interference aware eigenbeamforming according to embodiments.The illustrated process of FIG. 4A may be performed by an apparatus (orcomputing device) for performing beamforming optimization (i.e., forcalculating optimal beamforming weights). Said apparatus may bespecifically a distributed unit of a distributed access node (e.g., thedistributed unit 220 of FIG. 2). It is assumed that the apparatus isconnected electrically (e.g., via an optical fiber connection) to two ormore remote radio units of the distributed access node.

The illustrated process of FIG. 5 may correspond, similar to FIGS. 4Aand 4B, to one embodiment of the process discussed in relation to block302 of FIG. 3. Also similar to FIGS. 4A and 4B, it is, initially,assumed that the apparatus maintains channel state in-formation (CSI) ofa plurality of radio channels between two or more distributed radiounits and a plurality of terminal devices in a database. The channelstate information maintained in the database is assumed to comprise atleast (first and) second order statistics of the plurality of radiochannels.

Referring to FIG. 5, the actions illustrated by blocks 501 to 504 may beperformed separately for each remote radio unit of the two or moreremote radio units (similar to as discussed in relation to FIGS. 4A and4B). In the following, the process is discussed for a single remoteradio unit for simplicity. Block 501 may correspond to block 411 of FIG.4B and is, thus, not discussed here (again) for brevity. After thematrix

$( {I + {\sum\limits_{i}{\frac{\lambda_{i}}{\delta^{2}}R_{i}}}} )^{- 1}R_{k}$has been calculated for all k (i.e., for all of the plurality ofterminal devices) in block 501, the apparatus finds, in block 502, nlargest eigenvalues of (I+Σ_(i)λ_(i)/δ² R_(i))⁻¹ R_(k) separately foreach k indicating the kth terminal device of said plurality of terminaldevices. Here, n is an integer larger than one. Furthermore, theapparatus finds, in block 503, for each of the n largest eigenvalues, acorresponding eigenvector. Each eigenvector corresponds, here, to a setof optimal beamforming weights for a MIMO layer of a terminal device ofsaid at least one terminal device. In other words, the n eigenvectorsfound in block 503 for a certain terminal device are orthogonaleigenvectors for that terminal device. Thus, by selecting severallargest eigenvector, one gets several orthogonal beams for separate MIMOlayers. This property is enabled by the fact that the provided solutionaccording to embodiments works with correlation matrices which, bydefinition, have a rank which is larger than one.

In some embodiments, the n largest eigenvalues and correspondingeigenvectors may be calculated, in blocks 502, 503, only for some of theplurality of terminal devices (i.e., for at least one terminal device ofthe plurality of terminal devices) and only for some of the two or moreremote radio units (i.e., for at least one remote radio unit of the twoor more remote radio units). In other words, blocks 502, 503 may becarried out for at least one combination of a terminal device of theplurality of terminal devices and a remote radio unit of the two or moreremote radio units. For the other combinations of a terminal device andremote radio unit, only the largest eigenvalue may be calculated inblock 502 and a single corresponding eigenvector may be calculated inblock 503, similar to as discussed in relation to FIG. 4B.

Once multiple eigenvectors have been calculated, in block 503, for theplurality of terminal devices (or for at least some of them), theapparatus performs, in block 504, rank selection for the plurality ofterminal device (or at least for at least one terminal device of theplurality of terminal devices) based on results of the optimization. Inother words, the apparatus may determine, in block 504, how many MIMOstreams (i.e., how many orthogonal beams) should be used fortransmission to a given terminal device. This determination may be basedon, e.g., values (or magnitudes) of the calculated eigenvalues. Forexample, if the ratio between the largest and second largest eigenvaluesfor a given terminal device is not too large (i.e., said ratio is belowa certain pre-defined limit), a high-quality channel for a higher rank(higher SU-MIMO order) may be determined to be available in block 504and thus may be used for transmission. In other words, beamformingweights defined by the eigenvectors associated with the largesteigenvalue and the second largest eigenvalue are used for transmissionto the corresponding terminal device. In general (with n being anyinteger larger than one), the aforementioned ratio for lth largesteigenvalue may be calculated as a ratio between the largest eigenvalueand lth largest eigenvalue, where l is an integer larger than one. Insome embodiments, the rank for each of the plurality of terminal devices(or at least some of them) may be pre-defined.

After block 504 (that is, after the process described above has beencarried out for each remote radio unit), the process proceeds to block304 of FIG. 3, that is, to the single-user MIMO optimization betweendifferent remote radio units. All of the pre-coding vectors selectedthrough rank selection in block 504 may be taken into account in thesingle-user MIMO optimization in block 304 of FIG. 3.

At least some of the processes discussed in relation to FIGS. 3, 4A, 4Band 5 may be carried out in parallel with each other and/or in differentorder as presented above.

The blocks, related functions, and information exchanges described aboveby means of FIGS. 3, 4A, 4B and 5 are in no absolute chronologicalorder, and some of them may be performed simultaneously or in an orderdiffering from the given one. Other functions can also be executedbetween them or within them, and other information may be sent, and/orother rules applied. Some of the blocks or part of the blocks or one ormore pieces of information can also be left out or replaced by acorresponding block or part of the block or one or more pieces ofinformation.

FIG. 6 provides an apparatus 601 at least for performing beamformingoptimization. Specifically, FIG. 6 may illustrate an access node (or asub-unit thereof) for performing beamforming optimization andbeamforming itself. In some embodiments, the apparatus 601 maycorrespond to the access node 104 of FIG. 1 (or a part thereof). FIG. 6may, alternatively or more specifically, illustrate a distributed unitof a distributed access node (e.g., a distributed gNB).

The apparatus 601 may comprise one or more communication controlcircuitry 620, such as at least one processor, and at least one memory630, including one or more algorithms 631, such as a computer programcode (software) wherein the at least one memory and the computer programcode (software) are configured, with the at least one processor, tocause the apparatus to carry out any one of the exemplifiedfunctionalities of the apparatus (i.e., of the distributed unit of anaccess node) described above. Said at least one memory 630 may alsocomprise at least one database 632.

Referring to FIG. 6, the one or more communication control circuitry 620comprise at least beamforming optimization circuitry 621 which isconfigured to optimize beamforming weights associated with transmissionto a plurality of terminal devices and cause (i.e., at least trigger andpossibly also perform) beamforming based on results of the optimization.To this end, the beamforming optimization circuitry 621 is configured tocarry out at least some of the functionalities described above by meansof any of FIGS. 3, 4A, 4B and 5 using one or more individualcircuitries.

In some embodiments, the one or more communication control circuitry 620may further comprise beamforming circuitry for performing thebeamforming (i.e., actually forming beams and transmitting data usingsaid beams, as opposed to merely determining optimal beamformingweights). This may be the case, namely, if the apparatus corresponds toan access node or specifically a distributed access node comprising atleast one centralized unit, at least one distributed unit and at leasttwo remote radio units.

Referring to FIG. 6, the memory 630 may be implemented using anysuitable data storage technology, such as semiconductor based memorydevices, flash memory, magnetic memory devices and systems, opticalmemory devices and systems, fixed memory and removable memory.

Referring to FIG. 6, the apparatus 601 may further comprise differentinterfaces 610 such as one or more signaling interfaces (TX/RX)comprising hardware and/or software for realizing communicationconnectivity according to one or more communication protocols.Specifically, if the apparatus 601 corresponds to a distributed unit ofan access node, the one or more signaling interfaces 610 may comprise,for example, interfaces providing a connection to two or more remoteradio units, at least one centralized unit of the access node, one ormore other access nodes (or sub-units therein) and/or to one or more(external) computing devices. The one or more signaling interfaces 610may provide the apparatus with communication capabilities to communicate(possibly via one or more computing devices such as an access node) in acellular or wireless communication system, to access the Internet and acore network of a wireless communications network and/or to enablecommunication between user devices (terminal devices) and differentnetwork nodes or elements, for example. The one or more signalinginterfaces 610 may comprise standard well-known components such as anamplifier, filter, frequency-converter, (de)modulator, andencoder/decoder circuitries, controlled by the corresponding controllingunits, and one or more antennas.

As used in this application, the term ‘circuitry’ may refer to one ormore or all of the following: (a) hardware-only circuit implementations,such as implementations in only analog and/or digital circuitry, and (b)combinations of hardware circuits and software (and/or firmware), suchas (as applicable): (i) a combination of analog and/or digital hardwarecircuit(s) with software/firmware and (ii) any portions of hardwareprocessor(s) with software, including digital signal processor(s),software, and memory(ies) that work together to cause an apparatus, suchas a terminal device or an access node, to perform various functions,and (c) hardware circuit(s) and processor(s), such as amicroprocessor(s) or a portion of a microprocessor(s), that requiressoftware (e.g. firmware) for operation, but the software may not bepresent when it is not needed for operation. This definition of‘circuitry’ applies to all uses of this term in this application,including any claims. As a further example, as used in this application,the term ‘circuitry’ also covers an implementation of merely a hardwarecircuit or processor (or multiple processors) or a portion of a hardwarecircuit or processor and its (or their) accompanying software and/orfirmware. The term ‘circuitry’ also covers, for example and ifapplicable to the particular claim element, a baseband integratedcircuit for an access node or a terminal device or other computing ornetwork device.

In an embodiment, at least some of the processes described in connectionwith FIGS. 3, 4A, 4B and 5 may be carried out by an apparatus comprisingcorresponding means for carrying out at least some of the describedprocesses. Some example means for carrying out the processes may includeat least one of the following: detector, processor (including dual-coreand multiple-core processors), digital signal processor, controller,receiver, transmitter, encoder, decoder, memory, RAM, ROM, software,firmware, display, user interface, display circuitry, user interfacecircuitry, user interface software, display software, circuit, antenna,antenna circuitry, and circuitry. In an embodiment, the at least oneprocessor, the memory, and the computer program code form processingmeans or comprises one or more computer program code portions forcarrying out one or more operations according to any one of theembodiments of FIGS. 3, 4A, 4B and 5 or operations thereof.

Embodiments as described may also be carried out in the form of acomputer process defined by a computer program or portions thereof.

Embodiments of the methods described in connection with FIGS. 3, 4A, 4Band 5 may be carried out by executing at least one portion of a computerprogram comprising corresponding instructions. The computer program maybe provided as a computer readable medium comprising programinstructions stored thereon or as a non-transitory computer readablemedium comprising program instructions stored thereon. The computerprogram may be in source code form, object code form, or in someintermediate form, and it may be stored in some sort of carrier, whichmay be any entity or device capable of carrying the program. Forexample, the computer program may be stored on a computer programdistribution medium readable by a computer or a processor. The computerprogram medium may be, for example but not limited to, a record medium,computer memory, read-only memory, electrical carrier signal,telecommunications signal, and software distribution package, forexample. The computer program medium may be a non-transitory medium.Coding of software for carrying out the embodiments as shown anddescribed is well within the scope of a person of ordinary skill in theart.

Even though the embodiments have been described above with reference toexamples according to the accompanying drawings, it is clear that theembodiments are not restricted thereto but can be modified in severalways within the scope of the appended claims. Therefore, all words andexpressions should be interpreted broadly and they are intended toillustrate, not to restrict, the embodiment. It will be obvious to aperson skilled in the art that, as technology advances, the inventiveconcept can be implemented in various ways. Further, it is clear to aperson skilled in the art that the described embodiments may, but arenot required to, be combined with other embodiments in various ways.

The invention claimed is:
 1. An apparatus for performing beamformingoptimization for a distributed multiple-in multiple-out, MIMO,architecture, the apparatus comprising: at least one processor; and atleast one memory including computer program code, the at least onememory and the computer program code being configured, with the at leastone processor, to cause the apparatus to perform: maintaining, channelstate information of a plurality of radio channels, wherein each of theplurality of radio channels is between one of two or more radio units ofa distributed access node and one of a plurality of terminal devices andthe channel state information comprises first and second orderstatistics of the plurality of radio channels; calculating, separatelyfor each of the two or more radio units using an eigenbeamformingscheme, first sets of beamforming weights for forming beams fortransmitting from a corresponding remote radio unit to each of aplurality of terminal devices based on the second order statisticsassociated with the corresponding radio unit; performing, for eachterminal device of the plurality of terminal devices, single-user MIMOoptimization between the two or more radio units at least to maximize apre-defined metric based on all first sets of beamforming weightsassociated with transmission from the two or more radio units to acorresponding terminal device and on the first order statistics of radiochannels between each of the two or more radio units and thecorresponding terminal device, wherein the pre-defined metric is amutual information metric or signal-to-interference-plus-noise, SINR,and a result of the single-user MIMO optimization, for each terminaldevice, is a second set of beamforming weights to be applied fortransmission to said terminal device; and causing transmitting data,from the two or more radio units to the plurality of terminal devices,using beams formed by applying both first and second sets of optimizedbeamforming weights at the two or more radio units.
 2. The apparatusaccording to claim 1, wherein a signal y_(k) received at the kthterminal device of the plurality of terminal devices is modelled, in thesingle-user MIMO optimization, as:y _(k) ={tilde over (H)} _(k) T _(k) W _(k) x _(k) +n, wherein {tildeover (H)}_(k) is a combined channel matrix for the plurality of terminaldevices and the two or more remote radio units defined as {tilde over(H)}_(k)=[H_(k) ⁽¹⁾), . . . , H_(k) ^((M))] with H_(k) ^((m)) being thechannel matrix for the kth terminal device and mth radio unit and Mbeing the number of the two or more radio units, T_(k)=[t_(k) ⁽¹⁾; . . .; t_(k) ^((M))] with t_(k) ^((m)) being a pre-coding vector for the kthterminal device and mth radio unit defining a first set of beamformingweights, W_(k) is a second pre-coding vector for the kth terminal devicedefining a second set of beamforming weights, x_(k) is a transmit signalfor the kth terminal device, n is an additive receiver noise vector. 3.The apparatus according to claim 2, wherein the performing of thesingle-user MIMO optimization to maximize the pre-defined metric beingthe mutual information metric comprises, for each terminal device of theplurality of terminal devices: calculating a second set of beamformingweights W_(k,opt) asW _(k,opt)=_(W) _(k) ^(argmax) log(det(I+{tilde over (H)} _(k) T _(k) W_(k) W _(k) ^(H) T _(k) ^(H) {tilde over (H)} _(k) ^(H)), whereinlog(det (I+{tilde over (H)}_(k) T_(k)W_(k) W_(k) ^(H)T_(k) ^(H){tildeover (H)}_(k) ^(H))) is the mutual information metric.
 4. The apparatusaccording to claim 1, wherein the at least one memory and the computerprogram code are configured, with the at least one processor, to causethe apparatus to further perform: performing, for each terminal deviceof the plurality of terminal devices, further single-user MIMOoptimization to optimize power according to a water filling principle oran equal gain scheme.
 5. The apparatus according to claim 1, wherein theeigenbeamforming scheme is an eigenbeamforming scheme which does nottake into account multiuser interference.
 6. The apparatus according toclaim 1, wherein the eigenbeamforming scheme is an interference awareeigenbeamforming scheme, the calculating of the beamforming weightsusing the interference aware eigenperforming scheme comprising, for eachcombination of a radio unit of the two or more radio units and aterminal device of the plurality of terminal devices: performingoptimization to minimize total transmit power for transmission to theplurality of terminal devices subject to a pre-defined constraint on aminimum allowable expected value of SINR for the plurality of theterminal devices, wherein the total transmit power is defined, in theoptimization, based on sets of beamforming weights used for formingbeams for transmitting to the plurality of terminal devices and thepre-defined constraint is evaluated, in the optimization for each of theplurality of terminal devices, by calculating SINR values for a terminaldevice based on second order statistics for the terminal device and thesets of beamforming weights for the plurality of terminal devices. 7.The apparatus according to claim 6, wherein the second order statisticsof the plurality of radio channels comprise, for each of the pluralityof radio channels, a channel covariance matrix, said channel covariancematrix being used for calculating values of SINR for a correspondingterminal device for satisfying the pre-defined constraint.
 8. Theapparatus according to claim 6, wherein a signal y_(k) received at thekth terminal device of the plurality of terminal devices is modelled, inthe optimization for each remote radio unit of the two or more remoteradio units, as:${y_{k} = {{H_{k}t_{k}x_{k}} + {\sum\limits_{i \neq k}{H_{k}t_{i}x_{i}}} + n}},$wherein H_(k) is a channel matrix for the kth terminal device, t_(k) isa pre-coding vector for the kth terminal device defining a first set ofbeamforming weights, x_(k) is a transmit signal for the kth terminaldevice, n is an additive receiver noise vector and a sum of Σ_(i≠k)H_(k)t_(i)x_(i) is calculated over all but one of the plurality ofterminal devices.
 9. The apparatus according to claim 6, wherein theperforming of the optimization comprises solving, for each radio unit ofthe two or more remote radio units, an optimization problem formulatedas: $\min{\sum\limits_{i}{t_{i}}^{2}}$ subject${\gamma \leq {\frac{t_{k}^{H}R_{k}t_{k}}{{\sum\limits_{i \neq k}{t_{i}^{H}R_{k}t_{i}}} + \delta^{2}}\mspace{14mu}{for}\mspace{14mu}{all}\mspace{14mu} k}},$wherein i and k are indices indicating the ith and kth terminal deviceof the plurality of terminal device, t_(i/k) is a pre-coding vector forthe ith/kth terminal device defining a first set of beamforming weights,γ is the minimum allowable expected value of SINR, δ² is a noise term,R_(k) is a channel covariance matrix E(H_(k) ^(H)H_(k)) with H_(k) beinga complex non-deterministic channel matrix for the kth terminal device,E denoting an expected value and H denoting a conjugate transposeoperation, t_(k) ^(H) R_(k) t_(k) corresponding to a received desiredsignal power for the kth terminal device and Σ_(i≠k) t_(i)^(H)R_(k)t_(i) corresponding to a total received interference power forthe kth terminal device.
 10. The apparatus according to claim 6, whereinthe performing of the optimization, for each radio unit of the two ormore radio units, comprises solving an equivalent eigenvalue problemdefined through an equation:${{( {I + {\sum\limits_{i}{\frac{\lambda_{i}}{\delta^{2}}R_{i}}}} )^{- 1}R_{k}t_{k}} = {\frac{\delta^{2}}{\lambda_{k}}( \frac{\gamma + 1}{\gamma} )t_{k}}},$wherein i and k are indices indicating the ith and kth terminal deviceof the plurality of terminal device, t_(k) is a pre-coding vector forthe kth terminal device of the plurality of terminal device defining afirst set of beamforming weights, γ is the minimum allowable expectedvalue of SINR, δ² is a noise term, R_(k) is a channel covariance matrixE(H_(k) ^(H) H_(k)) with H_(k) being a complex non-deterministic channelmatrix for the kth terminal device, E denoting an expected value and Hdenoting a conjugate transpose operation, I is an identity matrix, λ_(i)is a Lagrangian multiplier for the ith terminal device relating to totaltransmit power P through Σ_(i)λ_(i)=Σ_(i)∥t_(i)∥²=P at optimal solution,the solving of said equivalent problem comprising: calculating, for eachk indicating the kth terminal device of the plurality of terminaldevices, a matrix defined as${( {I + {\sum\limits_{i}{\frac{\lambda_{i}}{\delta^{2}}R_{i}}}} )^{- 1}R_{k}};$finding, for each k indicating the kth terminal device of the pluralityof terminal devices, the largest eigenvalue of${( {I + {\sum\limits_{i}{\frac{\lambda_{i}}{\delta^{2}}R_{i}}}} )^{- 1}R_{k}},$wherein the largest eigenvalue for each index k corresponds to a minimumof the total transmit power while fulfilling the pre-defined constraint;and finding, for each largest eigenvalue, a corresponding eigenvector,wherein each eigenvector corresponds to a first set of optimalbeamforming weights for a terminal device of the plurality of terminaldevices.
 11. The apparatus according to claim 10, wherein the solving ofthe equivalent eigenvalue problem comprises, for at least onecombination of a terminal device of the plurality of terminal devicesand a radio unit of the two or more radio units: finding n largesteigenvalues of$( {I + {\sum\limits_{i}{\frac{\lambda_{i}}{\delta^{2}}R_{i}}}} )^{- 1}R_{k}$separately for each k indicating the kth terminal device of said atleast one terminal device, wherein n is an integer larger than one; andfinding, for each of the n largest eigenvalues, a correspondingeigenvector, wherein each eigenvector corresponds to a first set ofoptimal beamforming weights for a MIMO layer of a terminal device ofsaid at least one terminal device; and performing rank selection forsaid at least one terminal device based on results of the optimization.12. The apparatus according to claim 10, wherein the Lagrangianmultiplier λ_(k), for all k, has a pre-defined value.
 13. The apparatusaccording to claim 1, wherein the apparatus is a distributed unit of thedistributed access node and the causing of the transmitting of the datausing said beams comprises: transmitting first and second sets ofoptimized beamforming weights to the two or more radio units of thedistributed access node for performing beamforming by the two or moreradio units.
 14. A method, comprising: maintaining, in a database,channel state information of a plurality of radio channels, wherein eachof the plurality of radio channels is between one of two or more radiounits of a distributed access node and one of a plurality of terminaldevices and the channel state information comprises first and secondorder statistics of the plurality of radio channels; calculating,separately for each of the two or more radio units using aneigenbeamforming scheme, first sets of beamforming weights for formingbeams for transmitting from a corresponding radio unit to each of aplurality of terminal devices based on the second order statisticsassociated with the corresponding remote radio unit; performing, foreach terminal device of the plurality of terminal devices, single-userMIMO optimization between the two or more radio units at least tomaximize a pre-defined metric based on all first sets of beamformingweights associated with transmission from the two or more radio units toa corresponding terminal device and on the first order statistics ofradio channels between each of the two or more remote radio units andthe corresponding terminal device, wherein the pre-defined metric is amutual information metric or signal-to-interference-plus-noise, SINR,and a result of the single-user MIMO optimization, for each terminaldevice, is a second set of beamforming weights to be applied fortransmission to said terminal device; and causing transmitting data,from the two or more radio units to the plurality of terminal devices,using beams formed by applying both first and second sets of optimizedbeamforming weights at the two or more radio units.
 15. A computerprogram embodied on a non-transitory computer-readable medium, saidcomputer program comprising program instructions which, when executed onhardware, cause the hardware to perform at least: maintaining, in adatabase, channel state information of a plurality of radio channels,wherein each of the plurality of radio channels is between one of two ormore radio units of a distributed access node and one of a plurality ofterminal devices and the channel state information comprises first andsecond order statistics of the plurality of radio channels; calculating,separately for each of the two or more radio units using aneigenbeamforming scheme, first sets of beamforming weights for formingbeams for transmitting from a corresponding remote radio unit to each ofa plurality of terminal devices based on the second order statisticsassociated with the corresponding radio unit; performing, for eachterminal device of the plurality of terminal devices, single-user MIMOoptimization between the two or more radio units at least to maximize apre-defined metric based on all first sets of beamforming weightsassociated with transmission from the two or more radio units to acorresponding terminal device and on the first order statistics of radiochannels between each of the two or more radio units and thecorresponding terminal device, wherein the pre-defined metric is amutual information metric or signal-to-interference-plus-noise, SINR,and a result of the single-user MIMO optimization, for each terminaldevice, is a second set of beamforming weights to be applied fortransmission to said terminal device; and causing transmitting data,from the two or more radio units to the plurality of terminal devices,using beams formed by applying both first and second sets of optimizedbeamforming weights at the two or more radio units.